Professor Robert B.H. HauswaldKogod School of Business, AU
FIN 683Financial Institutions Management
Interest-Rate Risk
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Interest Rate Risk
• FIs (financial institutions or intermediaries) face two core risks– financial
– strategic
• Interest rate risk: changes in the term structure of interest rates (graph of time value of money)
– Federal Reserve monetary policy
– repricing model
– cricticisms and alternatives1/19/2016 Interest-Rate Risk © Robert B.H. Hauswald
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Future and Present Value
Today's Value of a Lump Sum or Stream of Cash Payments Received at a Future Point in Time
( )TT rPVFV +×= 1
T
T
r
FVPV
)1( +=
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Time Value of Money
• Present value PV = CFt/(1+r)t
• Future value FV = CFt(1+r)t
• Net present value NPV = sum of all PV
-PV 5 5 5 5 105
5
4
1 )1(
105
)1(
5
rrPV
tt +
++
=∑=
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∑= +
=T
tt
t
r
CPV
1 )1(
Zero coupon bond tr)1(
1000Price0 +
=
Term structure of interest rates ∑= +
=T
tt
t
t
r
CPV
1 )1(
Level-coupon (fixed-rate) bond
Bond/Loan Pricing
∑=
−++=
n
tt
tv
t
rr
CP
11)1()1(τ
periodmonthssixindays
couponnextandsettlementbetweendaysv =
With accrued interest:
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Price-Yield Relationship
• Price and yield (of a straight bond) move in opposite directions.
yield
price
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Parallel Yield-Curve Shifts
T
r
Current TS
Downward move
upward move
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Interest Rates and Net Worth
• FIs exposed to risk due to maturity mismatches between assets and liabilities– banks are either lenders or borrowers
– interest-rate exposure on both sides of B/S
– consequence:
• Interest-rate changes can have severe adverse impact on net worth: mismatches– thrifts, during 1980s
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US Treasury Bill Rate, 1965 - 2010
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Level & Movement of Interest Rates
• Federal Reserve Bank: U.S. central bank– FRB sets monetary policy
– controls which rate?
– conducts monetary policy how?
• Open market operations influence money supply, inflation, and interest rates
• Actions of Fed (December, 2008) in response to economic crisis– Target rate between 0.0 and ¼ percent
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Central Bank and Interest Rates
• Target is primarily short term rates– Focus on Fed Funds Rate in particular
• Interest rate changes and volatility increasingly transmitted from country to country– witness EU and Eurozone
– Fed actions can have dramatic effects on world interest rates
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Repricing Model
• Rate sensitivity means time to repricing– net interest income
• Repricing gap is the difference between the – accounting rate sensitivity of each asset and the
rate sensitivity of each liability: RSA - RSL
• Refinancing risk– but does it really measure refinancing risk?
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Maturity Buckets• Commercial banks must report repricing gaps
for assets and liabilities with maturities of:– One day
– More than one day to three months
– More than three months to six months
– More than six months to twelve months
– More than one year to five years
– Over five years
• Discretizing much more exact approaches
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Repricing Gap ExampleCum.
Assets Liabilities Gap Gap
1-day $ 20 $ 30 $-10 $-10
>1day-3mos. 30 40 -10 -20
>3mos.-6mos. 70 85 -15 -35
>6mos.-12mos. 90 70 +20 -15
>1yr.-5yrs. 40 30 +10 -5
>5 years 10 5 +5 0
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Repricing Model: Example 1
∆NII i = (GAPi) ∆Ri = (RSAi - RSLi) ∆Ri
• Individual gap: particular bucket
In the one day bucket, gap is -$10 million. If rates rise by 1%,
∆NII (1) = (-$10 million) × .01 = -$100,000
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Repricing Model: Example 2
• Cumulative gap
If we consider the cumulative 1-year gap,
∆NII = (CGAP) ∆R = (-$15 million)(.01)
= -$150,000
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Rate-Sensitive Assets
• Short-term consumer loans. If repriced at year-end, would just make one-year cutoff
• Three-month T-bills repriced on maturity every 3 months
• Six-month T-notes repriced on maturity every 6 months
• 30-year floating-rate mortgages repriced (rate reset) every 9 months1/19/2016 Interest-Rate Risk © Robert B.H. Hauswald
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Rate-Sensitive Liabilities
• RSLs bucketed in same manner as RSAs– same instruments
– but: different position
• Demand deposits and passbook savings accounts warrant special mention– generally considered rate-insensitive (act as
core deposits), but
– there are arguments for their inclusion as rate-sensitive liabilities
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CGAP Ratio: Cumulative Gap
• May be useful to express CGAP in ratio form as CGAP/Assets– Provides direction of exposure and
– Scale of the exposure
• Example: – CGAP/A = $15 million / $270 million = 0.56,
or 5.6 percent
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Equal Rate Changes on RSAs, RSLs
• Example: Suppose rates rise 2% for RSAs and RSLs. Expected annual change in NII,
∆NII = CGAP ×∆ R
= $15 million × .01
= $150,000
• With positive CGAP, rates and NII move in the same direction
• Change proportional to CGAP– but how do yields typically change?
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Unequal Changes in A&L Rates
• Yield curve: Term Structure of Interest Rates– short rates more volatile than long rates
– rising rates: yield curve flattens
– falling rates: yield curve steepens
• If changes in rates on RSAs and RSLs are not equal, the spread changes– in this case, still parallel shift but A&L rates differ
∆NII = (RSA ×∆ RRSA ) - (RSL ×∆ RRSL )
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Unequal Rate Change Example
• Spread effect example:
RSA rate rises by 1.2% and RSL rate rises by 1.0%
∆NII = ∆ interest revenue -∆ interest expense
= ($155 million × 1.2%) - ($155 million × 1.0%)
= $310,000
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Restructuring Assets & Liabilities
• FI can restructure assets and liabilitiestobenefit from projected interest rate changes– on or off the balance sheet: sell and buy, or
– pricing and terms of products: steer customers
• What does a FI need to strive for?– Positive gap: increase in rates increases NII
– Negative gap: decrease in rates increases NII
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Restructuring the Gap • Example: Harleysville Savings Financial
Corporation at the end of 2008– One year gap ratio was 1.45 percent
– Three year gap ratio was 3.97 percent
– If interest rates rose in 2009, it would experience large increases in net interest income
• What were they betting on? What happened?
• Commercial banks recently reducing gaps to decrease interest rate risk1/19/2016 Interest-Rate Risk © Robert B.H. Hauswald
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Weaknesses of Repricing Model
• Ignores market value effects of rate changes
• Overaggregative– Distribution of assets & liabilities within individual
buckets is not considered
– Mismatches within buckets can be substantial
• Ignores effects of runoffs: reinvestment risk– Bank continuously originates and retires consumer
and mortgage loans
– Runoffs may be rate-sensitive1/19/2016 Interest-Rate Risk © Robert B.H. Hauswald
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Off-Balance Sheet Issues
• Off-balance-sheet items are not included– Hedging effects of off-balance-sheet items not
captured
– Example: Futures contracts
• But: a lot of smaller FIs bet on interest rates– off-balance sheet: regulatory avoidance
• Repricing does not capture income effects
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Maturity of Portfolio• Maturity of portfolio of assets (liabilities)
– weighted average of maturities of individual components of the portfolio
• Maturity effects apply to portfolio as well as to individual assets or liabilities
• Typically, maturity gap, MA - ML > 0 for most banks and thrifts– sign of what function of FIs?
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Effects of Interest Rate Changes
• Size of the gap determines the size of interest rate change that would drive net worth to zero
• Immunization and effect of setting
MA - ML = 0
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Maturity Model
• Leverage also affects ability to eliminate interest rate risk using maturity model– Assets: $100 million in one-year 10-percent
bonds, funded with
– Liabilities: $90 million in one-year 10-percent deposits (and equity)
• Maturity gap is zero but exposure to interest rate risk is not zero.
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Repricing Model
• Repricing or funding gap model based on book value: difference between– interest income and expense: measures what?
– outdated but unfortunately widespread: small Fis
– book- not market-value based: meaningless
• Market value-based models: Bank for International Settlements (BIS)– maturity and duration models
1/19/2016 Interest-Rate Risk © Robert B.H. Hauswald
The Maturity Model
• Explicitly incorporates market value effects– maturity as a rough indicator of interest rate risk
• For fixed-income assets and liabilities:– Rise (fall) in interest rates leads to fall (rise) in
market price
– The longer the maturity, the greater the effect of interest rate changes on market price
– Fall in value of longer-term securities increases at diminishing rate for given increase in interest rates
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8% Coupon BondYield to Maturity T=1 yr. T=10 yr. T=20 yr.
8% 1,000.00 1,000.00 1,000.00
9% 990.64 934.96 907.99
Price Change 0.94% 6.50% 9.20%
Yield to Maturity T=1 yr. T=10 yr. T=20 yr.8% 924.56 456.39 208.29
9% 915.73 414.64 171.93
Price Change 0.96% 9.15% 17.46%
Zero Coupon Bond
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Maturities and Interest Rate Exposure
• If M A - ML = 0, is the FI immunized?– Liabilities: 1Y zero coupon bond with face value
$100. – Assets: 1Y loan, which pays back $99.99 shortly
after origination, and 1¢ at the end of the year. – Both have maturities of 1 year.
• Not immunized, – although maturity gap equals zero
• Reason: Differences in duration – coming soon
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Duration
• The average life of an asset or liability– also: its interest-rate (yield) sensitivity
• Defintion: the weighted-average time to maturity – using present value of the cash flows, relative to
– the total present value of the asset or liability as weights
1/19/2016 Interest-Rate Risk © Robert B.H. Hauswald
Summary
• Introduction to interest-rate risk– repricing model
– maturity model
• Widespread but not very helpful:– duration: market based DCF approach
– properly measures interest-rate exposure
• Why do we treat small and large FIs differently?– business model
– regulatory fragmentation, political economy 1/19/2016 Interest-Rate Risk © Robert B.H. Hauswald 35
Appendix: Yield Curves
• Yield curves: graphical representations of TVM as determined in FI markets
• Typical Shapes
• Typical explanations: hypotheses– expectations
– liquidity
– segmentation
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Term Structure of Interest Rates
Time to Maturity
Time to Maturity
Time to Maturity
Time to Maturity
YTMYTM
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Unbiased Expectations Theory
• Yield curve reflects market’s expectations of future short-term rates
• Long-term rates are geometric average of current and expected short-term rates
(1 +1RN)N = (1+ 1R1)[1+E(2r1)]…[1+E(Nr1)]
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Liquidity Premium Theory
• Allows for future uncertainty
• Premium required to hold long-term– impatience
– risk
– inflation
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Market Segmentation Theory
• Investors have specific needs in terms of maturity– clientele effects
• Yield curve reflects intersection of demand and supply of individual maturities
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Web Resources
• For information related to central bank policy, visit:
Bank for International Settlements www.bis.org
Federal Reserve Bank www.federalreserve.gov
1/19/2016 Interest-Rate Risk © Robert B.H. Hauswald